Thus, the inertial torque is almost equal and opposite to the contact torques on the trunk as a result of the fundamental laws of mechanics (see Equation 1 in Appendix A). The contact moments acting on the trunk will almost be equal and opposite to the inertial torques since the gravitational torque is minimal due to the upright trunk causing the gravity vector to pass close to the center-of-mass ( Fig. Thus, the sensitivity to a joint moment must always be considered in conjunction with the joint moment to assess the actual influence on the trunk angular acceleration. If the moment is low, and the sensitivity is high, the joint may not influence the trunk angular acceleration. It should be noted that when the trunk angular acceleration is sensitive to a moment, it does not imply that the moment is influencing the trunk angular acceleration. Similarly, an increase in a knee extension moment has the potential to cause an angular acceleration that leans the trunk posteriorly while an increase in hip flexion moment causes an angular acceleration that leans the trunk anteriorly. Thus, an increase in plantar flexion moment (a more negative ankle moment about the x-axis) can cause the trunk to have an angular acceleration that leans the trunk posteriorly (shoulders back relative to hips, which is a positive angular acceleration about the x-axis).
The sagittal plane trunk angular acceleration has a negative sensitivity to the moment generated at the ankle for most of the gait cycle ( Fig. Results and Discussion Trunk angular acceleration sensitivity Sagittal plane Note, to express the three-dimensional vectors in a sense that is most comparable with previously performed two-dimensional analysis, moments are expressed with reference to axes that remain parallel with the laboratory axes but with an origin at the proximal end of the corresponding segment (c.f., anatomically defined axes).
The laboratory axes have the x-axis directed to the subject’s right, the y-axis directed forward, and the z-axis directed vertically. This equation assumes a ball and socket joint for all joints. The joint constraints are defined by equation 4 in Appendix A. The equations of motion were derived using a standard d’Alembert approach and a sensitivity matrix relating the joint moments to trunk accelerations was derived (see Appendix A). Each segment’s inertial characteristics were defined using Visual 3D (C-motion, Germantown, Maryland). A 12 segment rigid body model consisted of two feet, shanks, thighs, forearms, and upper arms, a head, and a combined pelvis and trunk segment.
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